We consider a model in which shareholders provide a risk-averse CEO with risk-taking incentives in addition to effort incentives. We show that the optimal contract protects the CEO from losses for bad outcomes and is convex for medium outcomes and concave for good outcomes. We calibrate the model to data on 1,707 CEOs and show that it explains observed contracts much better than the standard model without risk-taking incentives. When we apply the model to contracts that consist of base salary, stock, and options, the results suggest that options should be issued in the money. Our model also helps us rationalize the universal use of at-the-money options when the tax code is taken into account. Moreover, we propose a new way of measuring risk-taking incentives in which the expected value added to the firm is traded off against the additional risk a CEO has to bear.

We analyze several proposals to restrict CEO compensation and calibrate two models of executive compensation that describe how firms would react to different types of restrictions. We find that many restrictions would have unintended consequences. Restrictions on total realized (ex-post) payouts lead to higher average compensation, higher rewards for mediocre performance, lower risk-taking incentives, and the fact that some CEOs would be better off with a restriction than without it. Restrictions on total ex-ante pay lead to a reduction in the firm's demand for CEO talent and effort. Restrictions on particular pay components, and especially on cash payouts, can be easily circumvented. While restrictions on option pay lead to lower risk-taking incentives, restrictions on incentive pay (stock and options) result in higher risk-taking incentives.